diff --git a/aesara/graph/fg.py b/aesara/graph/fg.py
index 7adde079fc..65e483d78e 100644
--- a/aesara/graph/fg.py
+++ b/aesara/graph/fg.py
@@ -465,19 +465,12 @@ def change_node_input(
             self.outputs[i] = new_var
         else:
             r = node.inputs[i]
-            if check:
-                if isinstance(r.type, aesara.sparse.SparseType):
-                    fail = not (
-                        isinstance(new_var.type, type(r.type))
-                        and r.type.dtype == r.type.dtype
-                    )
-                else:
-                    fail = not r.type.is_super(new_var.type)
-                if fail:
-                    raise TypeError(
-                        f"The type of the replacement ({new_var.type}) must be "
-                        f"compatible with the type of the original Variable ({r.type})."
-                    )
+            if check and not r.type.is_super(new_var.type):
+                raise TypeError(
+                    f"The type of the replacement ({new_var.type}) must be "
+                    f"compatible with the type of the original Variable ({r.type})."
+                )
+
             node.inputs[i] = new_var
 
         if r is new_var:
diff --git a/aesara/sparse/type.py b/aesara/sparse/type.py
index c26bb4d220..12d00fc627 100644
--- a/aesara/sparse/type.py
+++ b/aesara/sparse/type.py
@@ -150,12 +150,12 @@ def may_share_memory(a, b):
     def make_variable(self, name=None):
         return self.Variable(self, name=name)
 
-    def __eq__(self, other):
-        return (
-            super().__eq__(other)
-            and type(self) == type(other)
-            and other.format == self.format
-        )
+    # def __eq__(self, other):
+    #    return (
+    #        super().__eq__(other)
+    #        and type(self) == type(other)
+    #        and other.format == self.format
+    #    )
 
     def __hash__(self):
         return super().__hash__() ^ hash(self.format)
@@ -215,15 +215,24 @@ def value_zeros(self, shape):
 
         return matrix_constructor(shape, dtype=self.dtype)
 
+    def __eq__(self, other):
+        if type(self) != type(other):
+            return NotImplemented
+
+        return other.dtype == self.dtype and other.format == self.format
+
     def is_super(self, otype):
-        if (
-            isinstance(otype, type(self))
-            and otype.dtype == self.dtype
-            and otype.ndim == self.ndim
-            and self.format == otype.format
-        ):
+        # if (
+        #    isinstance(otype, SparseType)
+        #    and otype.dtype == self.dtype
+        #    and otype.ndim == self.ndim
+        #    and self.format == otype.format
+        #    and otype.broadcastable == self.broadcastable
+        # ):
+        #    return True
+        # return False
+        if self == otype:
             return True
-
         return False